Tue, March 28, 2017
Public Access

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March 2017
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10:00am [10:10am] Prof. Niranjan Balachandran
Time 10:15-11:00 Title: Bisecting and D-secting families for hypergraphs Abstract: Let n be any positive integer, [n]:={1,2,...,n}, and suppose $D\subset\{-n,-n+1,..,-1,0,1,...,n}$. Let F be a family of subsets of [n]. A family F' of subsets of [n] is said to be D-secting for F if for every A in the family F, there exists a subset A' in F' such that $|A\cap A'|-|A\cap ([n]\setminus A')| = i$, for some $i\in D$. A D-secting family F' of F, where D = {-1,0,1}, is a bisecting family ensuring the existence of a subset $A'\in F'$ such that $|A\cap A'|\in{\lfloor |A|/2\rfloor, \lceil |A|/2\rceil\}$ for each $A\in F$. We consider the problem of determining minimal D-secting families F' for certain families F and some related questions. This is based on joint work with Rogers Mathew, Tapas Mishra, and Sudebkumar Prashant Pal.

11:00am [11:00am] Sanjoy Pusti
Time 11.00 AM -11.45 AM Title: Ramanujan's Master theorem for radial sections of line bundles over the real hyperbolic space Abstract: Ramanujan's master theorem states that under suitable conditions, the Mellin transfrom of an alternating power series provides an interpolation formula for the coefficients of this power series. Ramanujan applied this theorem to compute several definite integrals and power series and this explains why it is referred as "Master Theorem". In this talk we shall try to explain its analogue for radial sections of line bundles over the real hyperbolic space. This a joint work (in progress) with Prof. Swagato K Ray.

12:00pm [12:00pm] Dr. Madusudhan Manjunath (skype)
Time 12.00 noon -12.45 PM Title: Riemann-Roch, Alexander Duality and Free Resolutions. Abstract: The Riemann-Roch theorem is fundamental to algebraic geometry. In 2006, Baker and Norine discovered an analogue of the Riemann-Roch theorem for graphs. This theorem is not a mere analogue but has concrete relations with its algebro-geometric counterpart. Since its conception this topic has been explored in different directions, two significant directions are i. Connections to topics in discrete geometry and commutative algebra ii. As a tool to studying linear series on algebraic curves. We will provide a glimpse of these developments. Topics in commutative algebra such as Alexander duality and minimal free resolutions will make an appearance. This talk is based on my dissertation and joint work with i. Bernd Sturmfels, ii. Frank-Olaf Schreyer and John Wilmes and iii. an ongoing work with Alex Fink.